***edit: Sorry, I think I accidentally responded to an old post on page-1. Doh!
According to the instructions, you must leave air inside. I imagine without any air, you would run into leakage problems as internal temperature fluctuates. Higher temp = higher pressure. Without enough air to allow compression , you will hydro-lock and blow out the seals. Just like an off-road damper w/ too little air inside.
BTW: Air inside should be perfectly fine. When the diff is spinning, all the bubbles will collect in the center away from the bevel gears as the dense fluid is spun to the outside via centripetal acceleration (mistakenly referred to as centrifugal force).
I was thinking of cavitation being the main culprit here; If you completely break grip and one wheel is stationary while the other is in full-slip, you're gonna have a lot of spin inside that housing. 1:1 diffs have vanes and pockets to assume the extra volume, but Tamiya seems to have solved this issue by just having you partially fill the housing. Occam's Razor I guess?